

A054799


Integers n such that sigma(n+2) = sigma(n) + 2, where sigma = A000203, the sum of divisors of n.


18



3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 434, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Only 3 composite numbers are known: 434, 8575, 8825. This sequence is the union of A050507 and A001359.


REFERENCES

Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions., M.Dekker Inc., New York, Problem 12 in Chapter V., p. 81.


LINKS



EXAMPLE

n = 434, divisors = {1, 2, 7, 14, 31, 62, 217, 434}, sigma(434) = 768, sigma(436) = 770; n = 8575, divisors = {1, 5, 7, 25, 35, 49, 175, 245, 343, 1225, 1715, 8575}, sigma(8575) = 12400, sigma(8577) = 12402; n = 8825, divisors = {1, 5, 25, 353, 1765, 8825}, sigma(8525) = 10974, sigma(8527) = 10976.


MATHEMATICA

Select[Range[1500], DivisorSigma[1, #+2]==DivisorSigma[1, #]+2&] (* Jayanta Basu, May 01 2013 *)


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



